Baby wipes for general body hygiene. After the armpits are cleaned, apply deodorant just like you would at home. There are many traveler sized deodorant sticks that take little space or weight in any pack. As for the possibility of deodorant attracting bears...after a lifetime of outdoor travels and adventures, this is not on my list or radar of possibles that I worry about.
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Earth and sky, woods and fields, lakes and rivers, the mountain and the sea, are excellent schoolmasters, and teach some of us more than we can ever learn from books.

John Lubbock